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HO E3AQR2P031-000-1

Technical Training

MEASUREMENT AND CALIBRATION HANDBOOK

Precision Measurement Equipment Laboratory Specialist Course

May 1997

81st TRAINING GROUP

336 Training Squadron

Keesler Air Force Base, Mississippi 39534-2480

Designed for AETC Course Use

NOT INTENDED FOR USE ON THE JOB AETC FORM 214, JAN 96 PREVIOUS EDITIONS ARE OBSOLETE STANDARD COVERSHEET

336th Training Squadron HO E3AQR2P031 000-1 Keesler Air Force Base, Mississippi 39534-2480 May 1997

i

Philosophy

The philosophy of the group emerges from a deep concern for the individual armed forces men and women and the need to provide highly trained and motivated personnel to sustain the mission of the Armed Forces. We believe the abilities, worth, self-respect, and dignity of each student must be fully recognized. We believe each be provided the opportunity to pursue and master an occupational specialty to the full extent of the individual's capabilities and aspirations for the immediate and continuing benefit of the individual, the Armed Forces, DoD and the country. To these ends, we provide opportunities for individual development of initial technical proficiencies, on-the-job training in challenging job assignments, and follow-on growth as supervisors. In support of this individual development, and to facilitate maximum growth of its students, the group encourages and supports the professional development of its faculty and administrators, and actively promotes innovation through research and the sharing of concepts and material with other educational institutions.

Acknowledgment

The material contained in this handbook has been a combined effort of the staff of

the Metrology Training Flight. Special thanks goes to SSgt Paul Ramseyer(Physical Dimensional Course) for his concerted efforts to compile the majority of this data.

Editorial Note

This guide has been established as a training aid for student attending all Metrology Courses. As technology changes, so must we. Should you encounter any additions, corrections, or deletions from this guide, please forward your suggestions to the following address :

336 TRS/TTMZT 709 Meadows Drive Ste. 255 Keesler AFB, MS 39534-2480

Mark your envelope : ATTN Mr. R. Stubblefield

You may also contact the course directly at DSN 597-9695 or commercial (601)

377-9695

This document was merged together from two documents HO E3AQR2P031-000 January 1996 and HO E3AZR2P051 008/009/010/011 September 1995 by SSG Paul E Ramseyer, for distribution among US Air Force and US Army calibration teams. DSN 597-0746 or 601 377-0746, Email [email protected], http://www.datasync.com/~ramseyer

Table of Contents


ii

I. GENERAL INFORMATION 1 CONVERSION FACTORS 4 MATHEMATICAL SYMBOLS 9 GREEK ALPHABET 10 POWER OF TEN MULTIPLIER CHART 11 POWER of TEN CONVERSION CHART 12 BINARY CONVERSION 13 II. MATHEMATICS 14 SEQUENCE OF MATHEMATICAL OPERATIONS 14 SIGNIFICANT FIGURES 14 ROUNDING OFF NUMBERS 14 EXPONENTS 15 INTERPOLATION 15 SCIENTIFIC NOTATION 15 NUMERICAL CONSTANTS (extended) 16 TRIGONOMETRY AND GEOMETRY 16 TRIGONOMETRIC RELATIONS 16 PYTHAGOREAN THEOREM 17 RADIAN MEASURE 18 VARIOUS MEASUREMENTS 18 ERROR CALCULATIONS 19 DIMENSIONAL ANALYSIS 20 DENSITIES OF VARIOUS SUBSTANCES 20 GRAVITATIONAL CORRECTION CHART 21 LINEAR COEFFICIENTS OF EXPANSION 22 GAGE BLOCK CLASSIFICATION 23 III. PHYSICAL-DIMENSIONAL TEMPERATURE 24 TEMPERATURE CONVERSION CHART 24 STEM CORRECTIONS 24 TEMPERATURE COMPARISON CHART 25 THERMOCOUPLE'S 25 THERMOCOUPLE IDENTIFICATION TABLE 26 THERMAL-SPECTRUM 27 RESISTANCE THERMOMETER 27 VOLUMETRIC COEFFICIENTS OF EXPANSION 28 BOYLES LAW 28 CHARLES LAW 28 IDEAL GAS LAW 29 HUMIDITY 29 DEW POINT 29 HUMIDITY 29


iii

FORCE 29 STRESS 29 STRAIN 30 YOUNG'S MODULUS 30 TRANSVERSE STRAIN 30 POISSON'S RATIO 30 HOOKE'S LAW 30 LOAD CELLS 30 TORQUE 30 COSINE ERROR 30 MASS and WEIGHT 31 REST POINTS 31 WEIGHING METHODS 31 DIRECT 31 SUBSTITUTION 31 TRANSPOSITION 31 DIFFERENTIAL WEIGHING 31 DENSITY, VISCOSITY AND FLOW 32 SPECIFIC GRAVITY 32 PYCNOMETER 32 SPECIFIC GRAVITY TABLES 33 SOLIDS 33 GASES 33 LIQUIDS 33 VISCOSITY 34 ABSOLUTE 34 KINEMATIC 34 VISCOMETER 34 FLOW 34 PRESSURE AND VACUUM 35 PRESSURE CONVERSION CHART 36 ROTARY MOTION 36 VIBRATION 37 IV. ELECTRONIC PRINCIPLES VOLTAGE, CURRENT, POWER DECIBELS AND POWER RATIOS... 38 RESISTOR, CAPACITOR COLOR CODES. 39 DIRECT CURRENT CALCULATIONS


iv

SERIES DC CIRCUITS. 44 PARALLEL DC CIRCUITS 44 DIVIDER NETWORKS... 45 BRIDGE CIRCUITS...... 45 ALTERNATING CURRENT CALCULATIONS SINE WAVE CONVERSION CHART 46 FREQUENCY AND PERIOD 46 WAVELENGTH... 46 PHASE ANGLE...... 46 TOTAL INDUCTANCE. 46 TOTAL CAPACITANCE 46 REACTANCE... 46 SERIES AC CIRCUITS... 47 PARALLEL AC CIRCUITS. 48 POWER... 49 BANDWIDTH... 49 RESONANCE... 49 TIME CONSTANTS... 49 TRANSFORMERS... 49 TIME CONSTANT CHART (CHARGE/DISCHARGE) 50 GLOSSARY 51

336th Training Squadron HO E3AQR2P031-000-1

Keesler Air Force Base, Mississippi 39534-2480 May 1997

1

GENERAL INFORMATION

CONVERSION FACTORS

MASS and WEIGHT

1 centigram = 0.1543 grains 0.01 grams

1 grain = 6.480 x 10

-2 grams

2.286 x 10-3

ounces

1 gram = 100 centigrams 980.7 dynes 15.43 grains 9.807 x 10

-5 joules/

cm 9.807 x 10

-3 joules/

meter(Newtons) 1.0 x 10

-3 kilograms

1,000 milligrams 0.03527 ounces 2.2046 x 10

-3 pounds

1 kilogram = 980,665 dynes 1000 grams 9.807 x 10

-2 joules/

cm 9.807 joules/meter (Newtons) 2.2046 pounds 9.842 x 10

-4 tons

(long) 1.102 x 10

-3 tons

(short)

1 ounce = 28.349527 grams 437.5 grains 16.0 drams 6.25 x 10

-2 pounds

1 ounce (fluid)= 2.957 x 10

-2 liters

1.805 cu. in.

1 pound = 0.4536 kilograms 7000 grains 453.5924 grams 256 drams 44.4823 x 10

4 dynes

4.448 x 10-2

joules/ cm 4.448 joules/meter (Newtons) 16.0 ounces 5.0 x 10

-4 tons (short)

LENGTH

1 angstrom = 1.0 x 10

-8 centimeters

1.0 x 10-10

meters 3.9370 x 10

-9 inches

1.0 x 10-4

microns

1 centimeter = 0.3937 inches 3.281 x 10

-2 feet

1.O94 x 10-2

yards 6.214 x 10

-6 miles

1 foot = 0.3333 yards 30.4801 centimeters 3.048 x 10

-4 kilometers

.3048 meters 1.645 x 10

-4 nautical

miles 1.894 x 10

-4 statute

miles

1 inch = 2.540 centimeters 8.33 x 10

-2 feet

2.778 x 10-2

yards 2.54 x 10

-2 meters

25.40 millimeters 25,400 microns

1 kilometer = 0.6214 statute miles 3280.8399 feet 1,094.0 yards 3.937 x 10

4 inches

1 knot = 1.0 nautical mile/hr

1 meter = 100 centimeters 39.37 inches 3.281 feet 1.094 yards 5.396 x 10

-4 nautical

miles 6.214 x 10

-4 statue

miles

1 micron = 1.0 x 10

-4 centimeters

1.0 x 10-6 meters

3.937 x 10-5 inches

1 nautical mile = 6076.1155 feet 1852.0 meters 1.1508 statute miles 2,027 yards

1 statute mile = 5280 feet 1.6093 kilometers 1760 yards 1.609 x 10

5 centimeters

6.336 x 104 inches

.8684 nautical miles

1 yard = 0.9l44 meters



2

3 feet 36 inches 91.44 centimeters 9.144 x 10

-4 kilometers 4.934 x 10

-4 nautical

miles 5.683 x 10

-4 statute

miles

VOLUME

1 in3 =

16.3871 cm3

5.787 x 10-4

ft3

1.639 x 10-5

m3

2.143 x 10-5

yd3

4.329 x 10-3

gallons (US Liq) 1.639 x 10

-2 liters

3.463 x 10-2

pints (US Liq)

1 ft3 =

2.832 x 10-2

m3

1728 in3

28,320 cm3

3.704 x 10-2

yd3

7.48052 gallons (US Liq) 28.32 liters 59.84 pints(US Liq) 29.92 quarts(US Liq)

1 yd3 =

0.7646 m3

27 ft3

7.646 x 105 cm

3

46,656 in3

202 gallons(US Liq) 764.5 liters 1615.9 pints(US Liq) 807.9 quarts(US Liq)

1 cm3 =

6.102 x 10-2

in3

3.5315 x 10-5

ft3

1.0 x 10-6

m3

1.308 x 10-6

yd3

2.642 x 10-4

gallons (US Liq) 1.0 x 10

-3 liters

2.113 x 10-3

pints (US Liq) 1.057 x 10

-3 quarts

(US Liq)

1 quart (US liquid) = 946.353 cm

3

57.75 in3

3.342 x10-2

ft3

9.464 x 10-4

m3

.25 gallons .9463 liters

1 liter = 1000 cm

3

3.531 x 10-2

ft3

61.02 in3

1.308 x 10-3

yd3

2.113 pints(US Liq) 1.0567 quarts (US Liq) .2642 gallons (US Liq)

1 gallon liquid = 231 in

3

3785.4118 cm3

0.13368 ft3

3.7853 x 10-3

m3

3.7853 liters

WEIGHT per VOLUME

1 gallon of water @4C 8.33585 lbs of water

PRESSURE

1 atmosphere @ 0C and

sea level = 14.696 PSIA

760 mmhg 29.9213 inhg

1 PSI (0C) = 51.7149 mmhg 2.036 inhg 6.8947 x 10

4 dynes/

cm2

1 inch of mercury (0C) =

.49116 pounds/in2

.03453 kilograms/cm

2

1 centimeter of mercury

(0C) = 13.5955 grams/cm

2

0.3937 inches of hg

1 g = 386 in/sec

2

1 millibar = 0.02953 in hg 0.0145 lbs/in

2

0.750062 mm hg

1 ft3 of water =

62.426321 lbs of water @39.2F 62.277354 lbs of water @60F

1 foot of water = .4335 lbs/in

2

.8826 in hg .03048 kgs/cm

2

1 foot of sea water = .4453 lbs/in

1 Torr = 1/760 atm. 1 mm 1000 microns

POWER, WORK and

HEAT CONVERSION

1 BTU = 251.9958 calories/ gram 777.649 ft-lbs



3

3.931 x 10-4 horse

power -hrs

1,054.8 joules

1 watt = 44.2537 ft-lbs/ minute 3.4144 BTU/hr 1 joule/sec

1 kilowatt = 1.3410 horsepower

1 horsepower = 745.7 watts 550 ft-lbs/sec 745.7 joules/sec

1 joule = 1.0 x 10

7 ergs =

0.2390 calories/gram

1 erg = 1 dyne/cm 7.3756 x 10

-8 ft-lbs

1 calorie/gram 4.184 joules



4

MATHEMATICAL SYMBOLS

+ Positive, Plus, or Add Perpendicular to

- Negative, Minus, or Subtract

Parallel to

or +/- Positive or Negative Plus or Minus

Pi

X or Multiply Base of natural log 2.718

or / Divide Square root

= or :: Equals 3

Cube root

Identical n

nth root

Not equal to n Absolute value of n

or Approximately equal to n n degrees

Greater than n' minutes of a degree feet or prime

Less than n" seconds of a degree inches or second

Greater than or equal to n Average value of n

Less than or equal to j Square root of -1

:: Proportional to

% Percentage

: Ratio

nl Subscript of n

Therefore

( ) Parentheses

Infinity

[ ] Brackets

Increment or change { } Braces

Angle

Vinculum



5

GREEK ALPHABET

NAME UPPER

CASE

COMMONLY DESIGNATES LOWER

CASE

COMMONLY DESIGNATES

Alpha A angles, area, absorption factor, atten. constant, I gain CB config.

Beta B angles, coefficients, phase constant, flux density, I gain CE config.

Gamma complex propagation constant angles, specific gravity, elect. conductivity, propag'n constant

Delta increment, determinant, permittivity, variation

angles, density, increment

Epsilon E base of natural logs, dielectric constant, electrical intensity

Zeta Z impedance coordinates, coefficients

Eta H hysteresis, coordinates, efficiency intrinsic impedance

Theta angular phase displacement, time constant, reluctance

Iota I current unit vector

Kappa K coupling coefficient, susceptibility, dielectric constant

Lambda permeance wavelength, attenuation constant

Mu M prefix micro, amplification factor, permeability

Nu N frequency, reluctivity

Xi coordinates, output coefficients

Omicron O reference point

Pi 3.1416

Rho resistively, volume charge density, coordinates

Sigma summation electrical conductivity, leakage coefficient, complex propag'n constant

Tau T time constant, time phase displacement, transmission factor, torque

Upsilon

Phi sealar potential, magnetic flux, radiant flux

phase angle

Chi angles, electrical susceptibility

Psi angles, coordinates, dielectric flux, phase difference

Omega resistance in ohms angular velocity (2pf)

POWER OF TEN MULTIPLIER CHART



6

Multiple or Submultiple

Symbol

Prefix Name

1012

= 1,000,000,000,000 T Tera Trillion

109 = 1,000,000,000 G Giga Billion

108 = 100,000,000 Hundred Million

107 = 10,000,000 Ten Million

106 = 1,000,000 M Mega Million

105 = 100,000 Hundred Thousand

104 = 10,000 Ten Thousand

103 = 1,000 K Kilo Thousand

102 = 100 H Hecto Hundred

101 = 10 D Deka Ten

100 = 1 One

10-1 = .1 d Deci One Tenth

10-2 = .01 c Centi One Hundredth

10-3 = .001 m Milli One Thousandth

10-4 = .0001 One Ten-Thousandth

10-5 = .00001 One Hundred-Thousandth

10-6 = .000001 Micro One Millionth

10-7 = .0000001 One Ten-Millionth

10-8 = .00000001 One Hundred-Millionth

10-9 = .000000001 n Nano One Billionth

10-12

= .000000000001 p Pico One Trillionth

10-15

= .000000000000001 f Femto One Quadrillionth

10-18

= .000000000000000001 a Atto One Quintillionth

POWER of TEN CONVERSION CHART



7

Move the decimal point the number of places and direction noted

To

From

t e r a

g i g a

m e g a

k i l o

b a s i c

d e c i

c e n t i

m i l l i

m i c r o

n a n o

p i c o

f e m t o

a t t o

Tera 3

6

9

12

13

14

15

18

21

24

27

30

Giga 3

3

6

9

10

11

12

15

18

21

24

27

Mega 6

3

3

6

7

8

9

12

15

18

21

24

kilo 9

6

3

3

4

5

6

9

12

15

18

21

basic 12

9

6

3

1

2

3

6

9

12

15

18

Deci 13

10

7

4

1

1

2

5

8

11

14

17

Centi 14

11

8

5

2

1

1

4

7

10

13

16

Milli 15

12

9

6

3

2

1

3

6

9

12

15

micro 18

15

12

9

6

5

4

3

3

6

9

12

Nano 21

18

15

12

9

8

7

6

3

3

6

9

pico 24

21

18

15

12

11

10

9

6

3

3

6

Femto

27

24

21

18

15

14

13

12

9

6

3

3

Atto 30

27

24

21

18

17

16

15

12

9

6

3

BINARY CONVERSION



8

29 2

8 2

7 2

6 2

5 2

4 2

3 2

2 2

1 2

0

512 256 128 64 32 16 8 4 2 1

EXAMPLE: 0 0 1 0 1 0 1 1 0 0 = 172

BINARY NUMBER

DECIMAL NUMBER

1 1

10 2

11 3

100 4

101 5

110 6

111 7

1000 8

1001 9

1010 10

110010 50

1100100 100

POWERS OF TWO

2n n 2

-n



9

1 0 1.0

2 1 0.5 POWERS OF TWO CHART

4 2 0.25

8 3 0.125

16 4 0.062 5

32 5 0.031 25

64 6 0.015 625

128 7 0.007 812 5

256 8 0.003 906 25

512 9 0.001 953 125

1 024 10 0.000 976 562 5

2 048 11 0.000 488 281 25

4 906 12 0.000 244 140 625

8 192 13 0.000 122 070 312 5

16 384 14 0.000 061 035 156 25

32 768 15 0.000 030 517 578 125

65 536 16 0.000 015 258 789 062 5

131 072 17 0.000 007 629 394 531 25

262 144 18 0.000 003 814 697 265 625

524 288 19 0.000 001 907 348 632 812 5

1 048 576 20 0.000 000 953 647 316 406 25

2 097 152 21 0.000 000 476 837 158 203 125

4 194 304 22 0.000 000 238 418 579 101 562 5

8 388 608 23 0.000 000 119 209 289 550 781 25

16 777 216 24 0.000 000 059 604 644 775 390 625

33 554 432 25 0.000 000 029 802 322 387 695 312 5

MATHEMATICS

SEQUENCE OF MATHEMATICAL OPERATIONS

Remember



10

Please Excuse My Dear Aunt Sally Parentheses (P) Exponents (E) Multiply (M) Divide (D) Add (A) Subtract (S)

SIGNIFICANT FIGURES/SIGNIFICANT DIGITS

Figures arrived at by counting are often exact. On the other hand, figures arrived at by measuring are approximate. Significant figures express the accuracy of the measurement.

When counting significant figures, all digits (including zeros) are counted EXCEPT those zeros that are to the left of the number. Example: 4.3 contains 2 significant figures/digits 0.0234 contains 3 significant figures/digits 0.1100 contains 4 significant figures/digits

ROUNDING OFF NUMBERS

Rule 1: If the first digit to the right of the last significant digit is a 6, 7, 8, or 9 round up by increasing the last significant digit by one and dropping all the following digits. (Example rounded off to three significant digits to the right of the decimal) 45.784624 becomes 45.785

Rule 2: If the first digit to the right of the last significant digit is a 0, 1, 2, 3, or 4, round down by leaving the last significant digit unchanged, and dropping all the following digits. (Example rounded off to two significant digits to the right of the decimal) 45.784624 becomes 45.78

Rule 3: If the first digit to the right of the last significant digit is a 5, and there are additional digits other than 0, round up by increasing the last significant digit by one, and dropping all the following digits. (Example rounded off to two significant digits to the right of the decimal) 7.1450004 becomes 7.15

Rule 4: If the first digit to the right of the last significant digit is a 5, and there are no additional digits other than 0, round to the nearest even digit. This rule is also known as the odd-even rule for rounding off numbers. (Example rounded off to two significant digits to the right of the decimal) 7.1450000 becomes 7.14

EXPONENTS

Zero exponent a =1

Negative exponent a-x1

ax



11

Multiplication a a ax y x y

Division a aa

aax y

x

y

x y

Power of a product ab a bx x x

Power of a power a axy

xy

Root of a power a ax

y x y ,

Fractional exponents a a1 4 4/ x

aa

y

xy

Radicals a

b

a

b ab a b

INTERPOLATION

To interpolate a value for any number in a given table

X =

mA A B BA A

1 2 1

2 1

+ 1B

X = unknown Am = measured amount A1 = lower of the two amounts bracketing the measured amount A2 = higher of the two amounts bracketing the measured amount B1 = value (from table) for A1 B2 = value (from table) for A2

SCIENTIFIC NOTATION

A whole number between 1 and 10 times the proper power of ten, also called standard form.

Example: 4.30 x 104



12

NUMERICAL CONSTANTS (extended)

or h = 3.14159 26535 89793 23846 26433 83279 50288 41971

or j = 2.71828 18284 59045 23536 02874 71352 66249 77572

TRIGONOMETRY AND GEOMETRY Remember:

H = Hypotenuse

A = Adjacent side

O = Opposite side

S = Sine

C = Cosine

T = Tangent

= angle between hypotenuse and adjacent side (base)

= angle between hypotenuse and the opposite side

sin O

A cosecant

H

O sin cos cos sececant

cos A

H sec ant

H

A cos sin sec cos ecant

tan O

A cot

A

O tan cot cot tanangent

TRIGONOMETRIC RELATIONS

Oscar

HadSick

O

HS

A

HeapCall

A

HC

Of

ApplesTomorrow

O

AH



13

PYTHAGOREAN THEOREM

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. c

2 = a

2 + b

2

a

2 = c

2 - b

2

b

2 = c

2 - a

2

LENGTH of SIDES for RIGHT-ANGLE TRIANGLES

Length of Hypotenuse = Side Opposite * Cosecant Side Opposite + Sine Side Adjacent * Secant Side Adjacent + Cosine Length of Side Opposite = Hypotenuse * Sine Hypotenuse + Cosecant Side Adjacent * Tangent Side Adjacent + Cotangent Length of Side Adjacent = Hypotenuse * Cosine Hypotenuse + Secant Side Opposite * Cotangent Side Opposite + Tangent

SIGNS OF THE FUNCTIONS

QUADRA sin cos tan

II

III

I

radius tangent



14

NT I + + + II + - - III - - + IV - + -

RADIAN MEASURE

The circular system of angular measurement is called radian measure. A radian is an angle that intercepts an arc equal in length to the radius of a circle as illustrated below.

Length of arc BC = radius of circle 6.28 radians = 360

2 radians = 360

radians = 180 1 radian = 57.2958 1 degree = 0.01745 radian

VARIOUS MEASUREMENTS

Plane figures bounded by straight lines.

Area of a triangle whose base is (b) and altitude (h).

area =bh

2

Area of a rectangle with sides (a) and (b).

area = ab

IV

cosine sine



15

Area of a parallelogram with side (b) and perpendicular distance to the parallel side (h).

area = bh

Plane figures bounded by curved lines.

Circumference of a circle whose radius is (r) and diameter (d)

circumference = 2r = d

Area of a circle

area = r2 = d

2 = .7854d

2

Length of an arc of a circle for an arc of degrees.

length of arc =r

180

ERROR CALCULATIONS



16

Relative Error

eM - T

Tr e N Ar

Where: er = relative error Where : er = Error

M = measured value N = Nominal TI Indicated

T = True value A = Actual STD Ind or Determined

Percent Relative Error Correction Factor

eM - T

Tr (%) 100 cf = A-N

Where: er(%) = percent relative error Where: cf = Correction Factor

M = measured value N = Nominal

T = true value A = Actual

The true value is usually replaced by the accepted or nominal value because the true value is

never exactly known.

Correction Factor (% and PPM)

CFA N

Nx%

100 CF

A N

Nxppm

106

WHERE : CF = Correction Factor (in Percent or Parts-Per-Million)

A = Actual Value

N = Nominal value

(1) To convert from Percent(%) to Parts-Per-Million, move the decimal place 4 places to the

right.

(2) To convert from Parts-Per-Million to Percent(%), move the decimal place 4 places to the

left.

Calculation of Acceptable Limits

_______% of Range (FULL SCALE) ________ Where any of these quantities are

______% of Reading(INPUT/OUTPUT) _______ given, cross multiply the values across,

______#of Digits(RESOLUTION) _______ and then add to fill the total block.

This TOTAL = ___________ value is then applied to the %READING

EXAMPLE : 930V applied, 1200 Volt Range, 8 1/2 digit display, tolerance (.015% input + .01%

range + 5 digits)



17

.01% Range * 1200 = .12

.015% Input * 930 = .1395

8 1/2 digits 1 2 0 0.0 0 0 0 5 (NOTE : ELIMINATE #s LEFT OF DECIMAL)

TOTAL = .25955 WHICH IS THEN APPLIED TO 930v FOR LIMITS OF 929.74045 to 930.25955

DIMENSIONAL ANALYSIS

80 80 60 87 78 ft

sec

ft

sec

12 in

1 ft

2.54 cm

1 in

1 m

100 cm

1 km

1000 m

60 sec

1 min

min

1 hr

km

hr

.

DENSITIES OF VARIOUS SUBSTANCES

(grams/cm3) D (lbs/in

3) Conditions

Acetone 0.792 0.02858778 20 C

Alcohol, ethyl 0.791 0.02858778 20 C

methyl 0.810 0.02922435 0 C

Carbon tetrachloride 1.595 0.05763852 20 C

Gasoline 0.66 - 0.69 0.0237267 - 0.0248841

Kerosene 0.82 0.02962944

Mercury 13.5955 .49116

Milk 1.028 - 1.035 0.03715254 - 0.03738402

Oils, Castor 0.969 0.03501135 15 C

Cotton seed .926 0.03344886 16 C

Lubricating .852 - .877 .0307 - .0318 15 C

Fuel .928 - .979 .0336 - .0353 15 C

Sea water 1.025 0.037031013 15 C

Turpentine (spirits) 0.87 0.03142341

Water 1.000 0.036128241 4 C



983 982

981 980

979 978 977

Gravity vs Latitude Elevation Chart

0 ft 2,000 ft 4,000 ft

6,000 ft 8,000 ft

NOTE gs

(Standard

Gravity) is

980.665

0 10 20 30 40 50 60 70 80 90

Latitude



19

LINEAR COEFFICIENTS OF EXPANSION

SUBSTANCE n X 10-6

C

n X 10-6

F

Aluminum 25.0 13.89

Brass (Yellow) 18.9 10.5

Chromium Carbide 8.1 4.5

Copper 16.6 9.22

Iron (Cast) 12.0 6.67

Nickel 13 7.22

Platinum 9.0 5.0

Steel (Hardened) 11.5 6.4

Steel (Carbon) 11.3 6.30

Tungsten 4.50 2.50

Tungsten Carbide 5.40 3.0

Zinc 35.0 19.4

Lf = Lo (1 + t) L = (Lo) () (t)

Where:

Lf = Length Final Lo = Length Original

L = Change in Length = Linear Coefficient of Expansion

t1 = Original Temperature t2 = Final Temperature

t = Change in Temperature (t2 - t1)



20

GAGE BLOCK CLASSIFICATION

Grade 0.5 Grade 1 Grade 2 Grade 3 Nominal Size(in)

Length Flatness & Parallelism




1 1 1 2 2 +4-2 4 +8-4 5

2 2 1 4 2 +8-4 4 +16-8 5

3 3 1 5 3 +10-5 4 +20-10 5

4 4 1 6 3 +12-6 4 +24-12 5

5 7 3 +14-7 4 +28-14 5

6 8 3 +16-8 4 +32-16 5

7 9 3 +18-9 4 +36-18 5

8 10 3 +20-10 4 +40-20 5

10 12 4 +24-12 5 +48-24 6

12 14 4 +28-14 5 +56-28 6

16 18 4 +36-18 5 +72-36 6

20 20 4 +40-20 5 +80-40 6

Gage Block Set No. 4-81 (Inch system)

.050 .102 .114 .126 .138 .150 .750

.100 .103 .115 .127 .139 .200 .800

.1001 .104 .116 .128 .140 .250 .850

.1002 .105 .117 .129 .141 .300 .900

.1003 .106 .118 .130 .142 .350 .950

.1004 .107 .119 .131 .143 .400 1.000

.1005 .108 .120 .132 .144 .450 2.000

.1006 .109 .121 .133 .145 .500 3.000

.1007 .110 .122 .134 .146 .550 4.000

.1008 .111 .123 .135 .147 .600

.1009 .112 .124 .136 .148 .650

.101 .113 .125 .137 .149 .700

Seven extra blocks used to make up an 88 Block set

.0625= 116

.078125= 564

.093750= 332

.109375= 764

.100025 .100050 .100075

Angle Block Sets

Set No. 6 6 Blocks, 1 deg. smallest increment

6 Blocks 1 3 5 15 30 45

Set No. 11 11 Blocks, 1 min. smallest increment

6 Blocks 1 3 5 15 30 45

5 Blocks 1 3 5 20 30

Set No. 16 16 Blocks, 1 sec. smallest increment

6 Blocks 1 3 5 15 30 45

5 Blocks 1 3 5 20 30 5 Blocks 1 3 5 20 30

TEMPERATURE



21

TEMPERATURE CONVERSION CHART

FROM TO FORMULA

FAHRENHEIT CELSIUS (F-32) 1.8

KELVIN (F+ 459.67) 1.8

RANKINE F + 459.67

RANKINE KELVIN R 1.8

CELSIUS (R- 491.67) 1.8

FAHRENHEIT R - 459.67

CELSIUS FAHRENHEIT ( .18C) + 32

RANKINE ( .18C)+ 491.67

KELVIN C + 273.15

KELVIN RANKINE 18. K

FAHRENHEIT ( .18K)- 459.67

CELSIUS K - 273.15

STEM CORRECTIONS

C = KN(t ti s )

C = Correction

K = Differential expansion coefficient between mercury and glass

K = .00016/C or K = .00009/ F

N = Number of thermometer scale degrees the mercury is out of the bath

ti = Temperature of the thermometer bulb

ts = Average temperature of the portion of the stem containing mercury which is out of

the bath

ta = Actual temperature

tt t

s1 2

2

t t K N t t a i i s

TEMPERATURE COMPARISON CHART



22

THERMOCOUPLE'S Et =

Er +

Em

Et = EMF value corresponding to the actual temperature at the Hot Junction

Er = EMF output of the thermocouple if one junction were at 0C and the other junction were

at a temperature equal to the one being used as the reference under discussion. Em = Measured EMF output of the couple in its configuration of use (that is, reference

junction not at 0C).



23

THERMOCOUPLE IDENTIFICATION TABLE

ANSI Code

Alloy Combination Color Coding Magnetic Lead

Temperature Range

EMF (mV)

Limits of Error (Whichever is greater)

+ Lead

- Lead

Thermocouple Grade (TG)

Extension Grade (EG)

Standard

Special

A B

(+)

C

(-)

A B

(+)

C

(-)

J IRON Fe

CONSTANTAN COPPER-NICKEL Cu-Ni

BRN WHT RED BLK WHT RED IRON (+) TG 0 to 750C

EG 0 to 200C

0 to 42.283

2.2C or .75%

1.1C or

.40%

K CHROMEL NICKEL-

CHROMIUM

Ni-Cr

ALUMEL NICKEL-ALUMEL

Ni-Al

BRN YEL RED YEL YEL RED ALUMEL (-)

TG -200 to 1250C

EG 0 to 200C

-5.973 to 50.633

2.2C or 0C 2.0%

1.1C or

.40%

T COPPER Cu


BRN BLU RED BLU BLU RED - TG -200 to 350C

EG -60 to

100C

-5.602 to 17.816

1.0C or 0C 1.5%

0.5C or

.40%

E CHROMEL NICKEL-

CHROMIUM

Ni-Cr


BRN PUR RED PUR PUR RED - TG -200 to 900C

EG 0 to 200C

-8.824 to 68.783

1.7C or 0C 1.0%

1.0C or

.40%

N* NICROSIL Ni-Cr-Si

NISIL Ni-Si-Mg

BRN ORN RED ORN ORN RED - TG -270 to 1300C

EG 0 to 200C

-4.345 to 47.502

2.2C or 0C 2.0%

1.1C or

.40%

R PLATINUM-

13% RHODIUM Pt-13% Rh

PLATINUM Pt

- - - GRN BLK RED - TG 0 to 1450C

EG 0 to 150C

0 to 16.741

1.5C or

.25%

.60C or

.10%

S PLATINUM-


PLATINUM Pt

- - - GRN BLK RED - TG 0 to 1450C

EG 0 to 150C

0 to 14.973

1.5C or

.25%

.60C or

.10%

B PLATINUM-


PLATINUM- 6% RHODIUM

Pt-6% Rh

- - - GRY GRY RED - TG 0 to 1700C

EG 0 to 100C

0 to 12.426



24

THERMAL-SPECTRUM

Celsius Fahrenheit Scale Scale 1410 2570 Silicon Melts 1083.4 1982.12 Copper Melts 1064.43 1947.974 Freezing Point of Gold 937.4 1719.32 Germanium Melts 961.93 1763.474 Freezing Point of Silver 660.37 1220.666 Aluminum Melts 630.74 1167.332 Silver Solder Melts 630.74 1167.332 Antimony Melts 444.674 832.4132 Boiling Point of Sulfur 216 420 50/50 Lead/Tin Solder Melts 156.61 313.898 Indium Melts 100 212 Steam Point at Sea Level 57.8 136.04 Highest Recorded World Temperature 37 98.6 Human Body Temperature 4 39.2 Maximum Density of Water 0.010 32.018 Triple Point of Water 0 32 Ice Point -38.87 -37.966 Mercury Freezes -78.5 -109.3 Sublimation Point of CO -88.3 -126.94 Lowest Recorded World Temperature -182.962 -297.3361 Oxygen Boils -273.15 -459.67 Absolute Zero

RESISTANCE THERMOMETER

R R A B t o t t 1 2

Rt = the resistance at some temperature (C) Ro = the resistance at 0C t = the temperature in C

A & B = constants for a particular element which best describe its behavior with temperature

RR =R

R

t

o

ID =1

RR RRt t-1

RR = Resistance Ratio Computed RRt = Resistance Ratio at a given temperature (t)

RR(t-1) = Resistance Ratio at temperature 1C below (t)

t = t RR - RR ID 2 2 t = the measured temperature t2 = the lower of two(2) temperatures from the table which bracket the resistance ratio computed

RR2 = Resistance Ratio at t2 ID = Inverse difference for the temperature which has the resistance ratio which is just greater than RR



25

VOLUMETRIC COEFFICIENTS OF EXPANSION

SUBSTANCE n 10

C

-4

n 10

F

-4

Alcohol, Ethyl 11.0 6.10

Benzene 13.9 7.70

Mercury 1.82 1.01

Petroleum (Pennsylvania) 9.0 5.0

Sulfuric Acid 5.56 3.10

Turpentine 9.70 5.40

Water 2.07 1.15

Vf = Vo (1 + t) V = (Vo) () (t) Where: Vf = Volume Final Vo = Volume Original

V = Change in Volume

= Volumetric Coefficient of Expansion

t = Change in Temperature (t2 - t1) t2 = Final Temperature t1 = Original Temperature

BOYLES LAW

The relationship between volume and pressure. Remember that the law assumes the temperature to be constant.

V

V

P

P

1

2

2

1

or V1P1 V2P2

V1 = original volume V2 = new volume P1 = original pressure P2 = new pressure

CHARLES LAW



26

The relationship between temperature and volume. Remember that the law assumes that the

pressure remains constant.

V

V

T

T or

V

T

V

T

1

2

2

1

1

2

2

1

V1 = original volume T1 = original absolute temperature V2 = new volume T2 = new absolute temperature

IDEAL GAS LAW

P V

T

P V

T

1 1

1

2 2

2

P1 = Initial Pressure V1= Initial Volume T1= Initial Temperature P2= Final Pressure V2= Final Volume T2= Final Temperature

HUMIDITY

DEW POINT

%RH =P t

P t

s dew

s a

100

Ps(ta) = the saturation pressure of the gas from a reference table at temperature ta Ps(tdew) = the saturation pressure of the gas from a reference table at temperature (tdew)

D = t ta w

D = Wet bulb depression ta = Dry bulb temperature tw = Wet bulb temperature

HUMIDITY



27

%RH =B

C

P

P

v

s

100 100

B = Pv = Pressure of the water vapor C = Ps = Saturation pressure % RH = Percent relative humidity

FORCE

STRESS

(sigma) =F

A

F = the force A = the area

STRAIN

(epsilon) =

D = change in length = original length

YOUNG'S MODULUS

Stress divided by strain.

Y = Y =F

A

Y =F

A =

F

AY

TRANSVERSE STRAIN

transverse =D

D

POISSON'S RATIO

Transverse strain to axial strain.



28

transverse

axial

DD

D =D

HOOKE'S LAW

F =YA

KX

K =YA

force constant

X = = elongation or change in length F = force

LOAD CELLS

F (lbs) =E

E (sens)C (lbs)0

s

Es = source voltage across the bridge Sen = sensitivity of the cell (mV/v) Eo = output voltage of the bridge C = range of the cell F = force acting on the cell

TORQUE

T = F S F = the force applied S = the distance through which the force is acting T = torque

COSINE ERROR

COS =side adjacent

hypotenuse

T = F S COS

MASS and WEIGHT R = Optical scale reading RP = Rest point



29

Msen = Sensitivity weight IRP = initial rest point FRP = final rest point SRP = sensitivity rest point mx = unknown mass ms = known mass Crs = correction of standard weight Crx = correction of test weight

= Difference not direction

REST POINTS

RP =

B +A + C

2 RP =

B + D

2

A C E

2

3

2

WEIGHING METHODS

DIRECT WEIGHING

m = RP SR SR =M

FRP -SRP

RP = FRP - IRP

m > : m m m

m < : m m m

sen

x x s

x x s

SUBSTITUTION WEIGHING

CR = SR IRP - FRP CRx s

ALWAYS ADD CRX TO THE NOMINAL VALUE OF MX.

TRANSPOSITION WEIGHING

CR SRIRP - FRP

2CRx s

ALWAYS ADD CRX TO THE NOMINAL VALUE OF MX.

DIFFERENTIAL WEIGHING

CR R - Mx sen

A, B, C, D, E = Values recorded for consecutive turning points



30

DENSITY, VISCOSITY AND FLOW

SPECIFIC GRAVITY

= Density in CGS system x = unknown substance D = Density in FPS system w = water W = Weight m = mass V = Volume a = air mass density of water at 4C = 1 gm/cm

3

weight density of water at 39.2F = .03612 lb/in3

weight density of water at 39.2F = 62.426321 lb/ft3

weight density of water at 60F = 62.277354 lb/ft3

sp. gr.=D

D sp. gr.=

sp. gr.=W

W W sp. gr.=

m

m m

x

w

x

a

a w

a

a w

w

sp. gr.=W W

W W sp. gr.=

m m

m m

a x

a w

a x

a w

V =W W

D a w

w

V =

m ma w

w

PYCNOMETER

Wp = weight of empty pycnometer vessel Wa = weight of pycnometer vessel and test liquid Wb = weight of pycnometer vessel and water

sp. gr.=W - W

W W

a p

b p

SPECIFIC GRAVITY TABLES

SOLIDS

Aluminum 2.7 Ice 0.917



31

Brass 8.2 - 8.7 Iron, Steel 7.6 - 7.8

Carbon 1.9 - 3.5 Lead 11.34

Copper 8.9 Oak 0.60 - 0.98

Gold 19.3 Pine 0.37 - 0.64

Human Body 1.07 Silver 10.5

GASES

Air 1.000 Neon 0.696

Ammonia 0.596 Nitrogen 0.967

Carbine dioxide 1.529 Oxygen 1.105

Hydrogen 0.069

LIQUIDS

Water, Distilled @ 4C 1.000 Mercury @ 0C 13.5951

Alcohol, Ethyl 0.789 Milk 1.029

Carbon Tetrachloride 1.60 Oil, Linseed 0.942

Gasoline 0.66 - 0.69 Water, Sea 1.025

Kerosene 0.82

VISCOSITY

ABSOLUTE

F

AV

L



32

= absolute viscosity F = force A = area

V = change in velocity

L = change in length (thickness)

KINEMATIC

= absolute viscosity

= density

= kinematic viscosity

MKS: =meter

sec FPS: =

ft

sec

2 2

VISCOMETER

V = k t

V = viscosity at temperature

k = instrument constant at temperature t = efflux time

FLOW

Q P

Z T

Q P

Z T

s s

s s

a a

a a

or QZ T P

Z T PQs

s s a

a a sa

or Q

Z T P

Z T PQa

a a s

s s as

Q = a volume or volume rate P = pressure (absolute) T = temperature (absolute) Z = compressibility factor (correction for non ideal gas behavior) a = actual s = standard

PRESSURE AND VACUUM

P =F

A

P = Pressure (lbs/in2, newtons/m

2, dynes/cm

2)

F = Force (lbs, Newtons, dynes)

A = Area (in2, m

2, cm

2)



33

P = gh

P = Pressure (lbs/in2, newtons/m

2, dynes/cm

2)

= the density of the fluid

h = the vertical height of the fluid

g = gravitational acceleration

P = Dh

P = Pressure (lbs/in2)

D = the weight density (lbs/in3)

h = the vertical height of the fluid

PT = true pressure M = mass

a = density of air

b = density of brass gL = local gravitational acceleration gS = standard gravitational acceleration Ao = area of piston b = pressure coefficient P = nominal pressure

k = coefficient of thermal expansion of piston

c = coefficient of thermal expansion of cylinder t1 = reference temperature t2 = ambient temperature

PRESSURE CONVERSION CHART

From/To

Psi in H2O ft H2O in HG ATM gm/cm2 kg/cm

2 cm H2O mm HG

1 Psi Multiply By

27.66 2.307 2.036 0.06805 70.31 0.07031 70.31 51.72

1 in H2O (4C)

0.03612 0.08333 0.07355 0.002458 2.540 0.002450 2.540 1.868

P

M

A

g

g

bP + t tt

o

l

s

c 2 1

1

1 1

a

b

k



34

1 ft H2O (4C)

0.4335 12.00 0.8826 0.02950 30.45 0.03048 30.48 22.42

1 in HG (0C)

0.49116 13.60 1.133 0.03342 34.53 0.03453 34.53 25.40

1 ATM 14.696 406.8 33.90 29.92 1033 1.033 1033 760

1 gm/cm2

0.01422 0.3937 0.03281 0.02896 0.0009678 0.0010 1.000 0.7356

1 km/cm2

14.22 393.7 32.81 28.96 0.9678 1000 1000 735.6111

1 cm H2O (4C)

0.01422 0.3937 0.03281 0.02896 0.0009678 1.000 0.0010 0.7355

1 mm HG (0C)

0.01934 0.5353 0.04461 0.03937 0.001316 1.360 0.001360 0.001360

Directions: Find the pressure unit you desire to convert from in the first left column. Follow the selected top row across to the corresponding unit you desire to convert to. Multiply the two numbers, the product is the pressure in the new unit.

ROTARY MOTION

t

= angular velocity (radians/second)

= angular displacement T = elapsed time

VIBRATION

f =1

T

V

DA

av2

g=.0512 f2 DA

Vav = average velocity f = frequency in hertz T = time in seconds g = acceleration in "g" units DA = double amplitude



35

Sens SensR R

ROC Loaded

1 2

2

SensOC = Open circuit sensitivity SensLoaded = Pickup sensitivity in the calibration load at frequency used R1 = Pickup impedance R2 = Pickup calibration load impedance

Sens SensR

R RCorr OC

3

1 3

SensCorr = Sensitivity into open circuit SensOC = Sensitivity corrected for loading effect R1 = Pickup impedance R3 = Input impedance on readout device

Sensitivity (mv) =2 mv (rms)

f DA

mV (RMS) = meter reading f = frequency in Hz DA = peak-to-peak displacement

VOLTAGE, CURRENT, POWER, and RESISTANCE RELATIONSHIP CHART

E

P

I

I R*

P

R

P R*

P

E

E

R



36

DECIBELS and POWER RATIOS

The ratio between any two amounts of electrical power is usually expressed in units on a

logarithmic scale. The decibel is a logarithmic unit for expressing a power ratio. Where : PR = power ratio in dB

PR(dB) = 10 log P

P

2

1

P1 = power in (small)

P2 = power out (large)

When the output of a circuit is larger than the input, the device is an AMPLIFIER and there is a GAIN. When the output of a circuit is less than the input, the device is an ATTENUATOR and there is a LOSS. In the last example , use the same formula as above and place the larger power over the smaller power, and put a minus sign in front of the PR to indicate a power loss or attenuation.

Basically, the decibel is a measure of the ratio of two powers. Since voltage and current are related to power by impedance, the decibel can be used to express voltage and current ratios, provided the input and output impedances are taken in to account.

Equal Impedances : dB = 20 log E

E

2

1

dB = 20 log I

I

2

1

Where: E1 = input voltage I1 = input current E2 = output voltage I2 = output current

Unequal Impedances: dB = 20 log E R

E R

2 1

1 2

dB = 20 log I R

I R

2 2

1 1

Where: R1 = impedance of the input in ohms R2 = impedance of the output in ohms E1 = voltage of the input in volts E2 = voltage of the output in volts I1 = current of the input in amperes I2 = current of the output in amperes

dB, Power, Voltage, Current Ratio Relationships

Decrease(-) Voltage and

Current Ratio

Decrease (-) Power Ratio

Number of dBs

Increase(+) Voltage and

Current Ratio

Increase (+) Power Ratio

1.0000 1.0000 0 1.0000 1.0000

.9886 .9772 .1 1.0120 1.0230

I R E

I

P

I 2

E

P

2

E I*

I R2 * E

R

2



37

.9772 .9550 .2 1.0230 1.0470

.9661 .9330 .3 1.0350 1.0720

.9550 .9120 .4 1.0470 1.0960

.9441 .8913 .5 1.0590 1.2220

.9333 .8710 .6 1.0720 1.1480

.9226 .8511 .7 1.0840 1.1750

.9120 .8318 .8 1.0960 1.2020

.9016 .8128 .9 1.1090 1.2300

.8913 .7943 1 1.1220 1.2590

.7943 .6310 2 1.2590 1.5850

.7079 .5012 3 1.4130 1.9950

.6310 .3981 4 1.5850 2.5120

.5623 .3162 5 1.7780 3.1620

.5012 .2512 6 1.9950 3.9810

.4467 .1995 7 2.2390 5.0120

.3981 .1585 8 2.5120 6.3100

.3548 .1259 9 2.8180 7.9430

.3162 .1000 10 3.1620 10.0000

.1000 .01000 20 10.0000 100.000

.03162 .0010 30 31.6200 1000.00

.0100 .0001 40 100.000 10000.0

.00316 .00001 50 316.20 1 x 105

.0010 1 x 10-6 60 1000.0 1 x 10

6

.000316 1 x 10-7 70 3162.0 1 x 10

7

dBm

The decibel does not represent actual power, but only a measure of power ratios. It is desirable to have a logarithmic expression that represents actual power. The dBm is such an expression and it represents power levels above and below one milli watt.

The dBm indicates an arbitrary power level with a base of one milli watt and is found by taking 10 times the log of the ratio of actual power to the reference power of one mill watt.

P(dBm) = 10 log P

mw1

where : P(dBm) = power in dBm P = actual power 1mw = reference power

READING COLOR CODES FOR RESISTORS AND CAPACITORS

RESISTORS



38

The charts on the following pages reflect how color codes are designated for both resistors and capacitors. While not every combination is shown, most popular color codes markings are indicated.

Some resistors have the ohmic value and tolerance printed right on the side of the resistor itself. It is easy to identify this type of resistor. The alpha-numeric code may be broken down as follows :

EXAMPLE : part number RN60D1001F

RN This code represents the type of resistor. This designation refers to a high stability,

fixed film resistor. Other designations are RCR (a carbon resistor) and RW (a fixed wire wound resistor)

60 This number represents the power rating of the resistor (wattage). In this case, the

power rating is 1/8 watt. Other examples are 10 (1/4 watt) and 25 (1 watt)

D This letter designates the temperature coefficient, usually stated in PPM/C. This

resistor has a temperature coefficient of 200 PPM/C.

1001 This is the ohmic value of the resistor. The last number in this group of numbers represents how many zeros are to be added to the remaining group of numbers. For 1001, the value is 100 ohms with one zero added to it, or 1000 ohms. Another example is 4023; this indicates 402 ohms with three zeros added, or 402,000 ohms. Another

code indicates fractional values. In 53R4, the R stands for a decimal place, so this value is 53.4 ohms.

F This code represents the tolerance of the resistor. The F is 1%. The other codes

used are as follows: G = 2%; J = 5%; K = 10%, and M = 20%.

Different marking schemes are used on capacitors mainly because of the varying needs fulfilled by the various capacitor types. Temperature coefficient is of minor importance in an electrolytic filter capacitor, but it is very important in ceramic trimmers for attenuator use. you never find temperature coefficient on an electrolytic label, but it is always present on ceramic trimmers.

CAPACITORS

CERAMIC DISC CAPACITORS: Information is usually printed. M = 20%

K = 10%

J = 5%

G = 2%

F = 1%

Capacitance is in pf. Capacitance tolerance is shown in percent or by letter. Temperature

coefficient is indicated by P200 which means +200ppm/C which means +200 P/M/C, or N100

for -100 P/M/C, etc.

CERAMIC TUBULAR CAPACITORS: These capacitors are usually white enamel coated with parallel radial leads and look like dog bones. The code consists of color dots which indicate temperature coefficient, capacitance, and tolerance



39

BUTTON MICA CAPACITORS: The most difficult part of reading the code on these capacitors is to remember to read the dots moving in a clockwise direction. The dots are usually printed more to one side than the other.

MOLDED MICA CAPACITORS: This was once a very popular type, rectangular with dots and arrow or similar directional indicator. Standard color code applies.

DIPPED MICA CAPACITORS: This type of capacitor has a printed label like that appearing on ceramic disk capacitors.

PAPER AND FILM CAPACITORS: Aluminum and tantalum electrolytic capacitors, in nearly all cases, have printed or stamped labels indicating capacitance, tolerance, and voltage ratings. Other characteristics are usually unimportant.

AIR TRIMMERS: The same information applies as with paper and film capacitors. Often, only the range is indicated.

COLOR CODE MARKING FOR RESISTORS

COMPOSITION TYPE RESISTORS

FILM TYPE RESISTORS A B C D E First Significant

Figure Second Terminal Significant figure Tolerance

Multiplier

NOTE : BANDS A THRU D ARE OF EQUAL WIDTH

Band A : The first significant figure of the resistance value.

A B C D E First Significant Figure Failure Rate Level (Established Second Significant Figure reliability types only) Tolerance

Multiplier



40

Band B : The second significant value of the resistance value.

Band C : The multiplier is the factor by which the two significant figures are multiplied to yield the nominal resistance value

Band D : The resistors tolerance

Band E : When used on composition resistors, band E indicates the established reliability failure rate level. On film resistors, this band is approximately 1.5 times the width of the other bands, and indicates type of terminal.

COLOR CODE CHART

BAND

A BAND

B BAND

C BAND

D BAND

E

COLOR 1st FIG

COLOR 2nd FIG

COLOR MULTIPLIER COLOR TOLERANCE COLOR FAIL RATE

TERMINAL

BLACK 0 BLACK 0 BLACK 1 SILVER 10% BROWN 1%

BROWN 1 BROWN 1 BROWN 10 GOLD 5% RED 0.1%

RED 2 RED 2 RED 100 RED 2 ORANGE 0.01%

ORANGE 3 ORANGE

3 ORANGE 1000 NONE 20% YELLOW 0.001%

YELLOW 4 YELLOW 4 YELLOW 10000 WHITE SOLDER

GREEN 5 GREEN 5 GREEN 100000

BLUE 6 BLUE 6 BLUE 1000000

PURPLE (VIOLET)

7 PURPLE (VIOLET)

7

GRAY 8 GRAY 8 SILVER 0.01

WHITE 9 WHITE 9 GOLD 0.1

Bad Booze Rots Our Young Guts But Vodka Goes Well



41

CAPACITOR COLOR CODES TYPE 1st A B C D E Digit 2nd Digit

A B C D E Multiplier Tolerance Characteristic or Class 1st Digit 2nd Digit Multiplier Tolerance No Color Voltage Rating

Voltage rating No Color A - Temperature Coefficient Tolerance B - 1st Digit C - 2nd Digit D - Multiplier E -Tolerance CAPACITANCE 1st Digit 2nd Digit Multiplier Multiplier 2nd Digit Tolerance 1st Digit

VOLTAGE 1st Digit 2nd Digit

D

C

B

B

C

D e

D



42

CAPACITOR COLOR CODE NUMBERING SYSTEMS

6-DOT RMA-JAN-AWS Standard Capacitor Color Code COLOR TYPE 1st

DIGIT 2nd DIGIT

MULTIPLIER TOLERANCE (percent)

CHARACTERISTIC or CLASS

Black JAN Mica 0 0 1

Brown 1 1 10 1 Applies to

Red 2 2 100 2 temperature

Orange 3 3 1000 3 coefficients or

Yellow 4 4 10000 4 methods of testing

Green 5 5 100000 5

Blue 6 6 1000000 6

Purple 7 7 10000000 7

Gray 8 8 100000000 8

White RMA mica 9 9 1000000000 9

Gold .1

Silver AWS paper .01 10

Body 20

5-Color Capacitor Color Code COLOR 1st

DIGIT 2nd DIGIT

MULTIPLIER TOLERANCE (percent)

VOLTAGE

Black 0 0 1

Brown 1 1 10 1 100

Red 2 2 100 2 200

Orange 3 3 1000 3 300

Yellow 4 4 10000 4 400

Green 5 5 100000 5 500

Blue 6 6 1000000 6 600

Purple 7 7 10000000 7 700

Gray 8 8 100000000 8 800

White 9 9 1000000000 9 900

Gold .1 1000

Silver .01 10 2000

Body 20

Ceramic Capacitor Color Code COLOR 1st

DIGIT 2nd DIGIT

MULTIPLIER TOLERANCE over 10pf

TOLERANCE under 10 pf

TEMPERATURE

Black 0 0 1 20% 2.0 pf 0

Brown 1 1 10 1% -30

Red 2 2 100 2% -80

Orange 3 3 1000 -150

Yellow 4 4 10000 -220

Green 5 5 5% 0.5 pf -330

Blue 6 6 -470

Purple 7 7 -750

Gray 8 8 .01 0.25 pf +30

White 9 9 .1 10% 1.0 pf +500 to -330

Gold aaaaa +100



43

DIRECT CURRENT (DC) CALCULATIONS

SERIES DC CIRCUITS Total resistance = the sum of the individual

resistances RT = R1 + R2 + R3 +.................... Total Voltage = the sum of the individual

voltage drops Ea = ER1 + ER2 + ER3 +................. Total Current is determined by the Total

Resistance (RT) of the circuit and Applied Voltage (Ea). It will be the same value at any point within the circuit.

It = IR! = IR2 = IR3 = ...................... Total Power = sum of all power losses in the

circuit. PT = PR1 + PR2 + PR3 + .................

PARALLEL DC CIRCUITS Total Resistance = the reciprocal of the sum

of the reciprocals. For Multiple Branches:

R

R R R

T

B B B

1

1 1 1

1 2 3

. .. . . . . . .

For branches of like value:

RR

Nt

B

B

Where RB = resistance of

one branch, NB=# of branches For Only Two Branches:

RR R

R Rt

B B

B B

1 2

1 2

*

Total Voltage is applied to each branch of a

parallel circuit

EA = EB1 = EB2 = EB3 = ................... Total current = sum of the current in the

individual branches.

It = It1 + It2 + It3 + ......................

Total Power = sum of all power

losses in the circuit

Pt = PR1 + PR2 + PR3 +.................



44

DIVIDER NETWORKS The division of voltage and current in a circuit can be determined in the following manner : Voltage Divider Current Divider

ER

R RER A1

1

1 2

( ) IR

R RIR t1

2

1 2

( )

BRIDGE CIRCUITS The relationships that exist in a bridge are indicated below

RR R

RX

V 1

2

( )

R

R

R

R

X

V

1

2

R

R

R

RX V

1 2

R R R RV X1 2( ) ( )

E

A

R

1 R

2 E

A R1 R

2

R

1

R

2

R

X

R

V

G



45

ALTERNATING CURRENT (AC) CALCULATIONS

SINE WAVE VOLTAGE CONVERSION CHART

TO

FROM Effective (RMS)(VAC)

Average Peak Peak-to-Peak

Effective (RMS)(VAC)

1 0.900 1.414 2.828

Average

1.110 1 1.571 3.142

Peak

0.707 0.637 1 2.000

Peak-to-Peak

0.354 0.318 0.500 1

FREQUENCY AND PERIOD(TIME)

fp

1

pf

1

WAVELENGTH

300 10

300 106

6* ( * )( )f

p

PHASE ANGLE

P

P

meas

tot

*3600

TOTAL INDUCTANCE TOTAL CAPACITANCE

SERIES SERIES

L L L LT 1 2 3 ............

C

C C C

T

1

1 1 1

1 2 3

.. .. ...

PARALLEL PARALLEL

REACTANCE

X FLL 2 X

FCC

1

2

SERIES RL SERIES RC

One Alternation

One Cycle(Period)

Eave Epeak Erms(Eeff) Epk-pk

00

1800

3600

600 120

0 240

0

3000

3

2

3

4

3

5

3

2 radians



46

I I IT R L

I I IT R C

Z R X L 2 2

Z R X C 2 2

E E EA R L 2 2

E E EA R C 2 2

IE

ZT

A IE

ZT

A

TANX

R

L1

TANX

R

C1

TANE

E

L

R

1

TANE

E

C

R

1

SERIES RCL

Z R X XL C 2 ( )

E E E EA R L C 2

( )

TE

ZT

A

TAN

X X

R

C L1

TAN

E E

E

C L

R

1

PARALLEL RC

PARALLEL RL

EL,XL EA,ZT

ER,R,IT=IC=IR EC,X

C

EA,ZT

ER,R,IT=IC=IR

EC,XC EA,ZT(Capacitively)

EL,XL EA,ZT(Inductively)

ER,R,IT=IL=IC=IR



47

E E EA R C

E E EA R L

I I IT R C 2 2

I I IT R L 2 2

ZE

I

A

T

ZE

I

A

T

tan 1I

I

C

R

tan 1I

I

L

R

PARALLEL RCL

E E E EA R L C

I I I IT R C L 2 2( )

ZE

I

A

T

tan 1

I I

I

C L

R

POWER

Q

TRUE POWER

SERIES

Ic

IT

IR,R,EA=EC=ER IL

IT

IR,R,EA=EL=ER

IL IT (INDUCTIVELY)

IC IT (CAPACITIVELY)

IR,R,EA=EC=EL=ER



48

P I RT R ( ) *2

Q

X

R

L

APPARENT POWER

P E IA A T ( )

PARALLEL

QR

X L

POWER FACTOR

PFP

P

T

A

cos

BANDWIDTH

BWf

Q

r SERIES BWf R

X

r

L

PARALLEL BWf X

R

r L

RESONANCE

fLC

r 1

2 C

f Lf

1

4 2 2 ( ) L

f Cr

1

4 2 2 ( )

RL TIME CONSTANTS

RC TIME CONSTANTS

TCL

R

TC R C *

#TCt

TC

# 'TC st

TC

TRANSFORMERS

N

N

E

E

I

I

P

S

P

S

S

P

( )

( )

N

N

Z

Z

P

S

P

S

2

2



49

CURVE

RC CIRCUIT RL CIRCUIT

A

CAPACITOR VOLTAGE ON CHARGE

INDUCTOR CURRENT OR RESISTOR VOLTAGE ON BUILD-UP

B

CAPACITOR VOLTAGE ON DISCHARGE RESISTOR VOLTAGE OR CAPACITOR CURRENT ON CHARGE OR DISCHARGE

INDUCTOR CURRENT OR RESISTOR VOLTAGE ON DECAY INDUCTOR VOLTAGE ON BUILD-UP OR DECAY

5 4 3 2 1 .5

100

9

0

80

70

60

50

40

30

20

10

0

A

B



50

GLOSSARY

aberration A broad term covering several types of image defects in a lens or lens system.

absolute pressure Actual pressure on a confined gas, irrespective of the atmosphere on the outside. Absolute pressure = gage pressure + atmospheric pressure.

absolute system A system of units in which a small number of units is chosen as fundamental and all other units are derived from this group.

absolute temperature Temperature measured from absolute zero as in the Kelvin and Rankine scales.

absolute zero (1) This is the temperature at which the volume of an ideal gas would become zero. The value calculated from the limited value of the coefficient of expansion of various real gases is -273.15C. (2) The temperature at which all thermal (molecular) motion ceases; zero point in absolute temperature scale equal to -273.15C or -459.69F. Absolute temperature T is given by the equation: 1/2 MV AV 2 = 3/2 kT

absorption (1) The loss of energy in traveling through a medium. Examples: A yellow filter absorbs all wavelengths except yellow just as red paint will absorb all colors except red which is reflected. (2) The internal taking up of one material by another. (3) Transformation of radiant energy into other forms of energy when passing through a material substance.

acceleration (1) A rate of change in velocity per unit time. Positive acceleration means an increase in velocity while negative acceleration means a decrease in velocity per unit time. Avoid the use of the term "deceleration." (2) The time rate of change of velocity in either magnitude or direction. CGS Unit: cm/sec .

acceleration due to gravity (g) The acceleration of a freely falling body in a vacuum, 980.665 cm/sec or 32.174 ft/sec at sea level and 45 latitude.

accommodation Changes in focus of the crystalline lens to adjust the eye for various object distances.

accuracy



51

The term accuracy refers to how close we are to the nominal value. In the past we have used this term to indicate error in a measurement device. For instance, the accuracy of a standard cell is plus or minus 0.01 percent. Use of the word accuracy in this sense is incorrect because what we mean is the inaccuracy or error is plus or minus 0.01 percent. However, this is still a common method of describing accuracys. To remedy this practice, the National Bureau of Standards has dropped the term accuracy, when used in this respect, and uses instead the term "uncertainty."

achromat A lens doublet, to two lenses combined to eliminate chromatic aberration.

achromatic Free from hue

activation energy The energy necessary to start a particular reaction.

actual value (true value) It is not possible to determine a completely true value of a quantity as there is always some error in every measurement. Theoretically we could say the "true" value of a measured quantity can be derived by taking the average of an infinite number of measurements assuming that the conditions contributing to deviations act is a completely free and random manner.

acuity Visual acuity is the resolving power of the eye, normally taken as 1 minute arc. Vernier acuity is the ability of the eye to make coincidence settings.

adsorption The adhesion of one substance to the surface of another.

algebra A continuation of arithmetic in which letters and symbols are used to represent definite quantities whose actual values may or may not be known.

algorithm Step-by-step procedure for the solution to a problem. First the problem is stated and the algorithm is devised for its solution.

alignment telescope A telescope specifically designed to be mounted and used in conjunction with an end target in order to form a fixed line of sight. Can also be used to measure linear displacement (alignment of a rail for straightness) by using the optical micrometers.

alloy A mixture of two or more metals, such as brass (zinc and copper), bronze (copper and tin), and manganin (nickel, manganese, and copper).

alnico An alloy consisting chiefly of aluminum, nickel, and cobalt. It has high retentivity and is used to make powerful small-size permanent magnets which hold their magnetism indefinitely.



52

alpha The current amplification factor when connected in a common base configuration.

alpha particle (1) Particle identical with a helium nucleus emitted from the nucleus of a radioactive atom. (2) A helium nucleus, consisting of two protons and two neutrons, with a double positive charge. Its mass is 4.002764 a Mu (mass units).

alpha ray A stream of fast-moving helium nuclei; a strongly ionizing and weakly penetrating radiation.

alphanumeric Set of all alphabetic and numeric characters.

alternation One half of a complete cycle, consisting of a complete rise and fall of voltage or current in one direction. There are 120 alternations per second in 60 Hz alternating current.

altimeter An aircraft instrument that indicates the elevation in respect to a reference. The aneroid altimeter is referenced to sea level, while an electronic altimeter uses the radar method. See barometer.

ambient temperature The temperature of the air in the immediate vicinity.

ambiguity The quality of having more than one meaning.

amici prism direct vision prism, beam of light is dispersed into a spectrum without mean deviation.

ammeter An instrument used for measuring the amount of current in amperes. A meter that indicates the current value in milli-amperes is a milli-ammeter, and one that indicates values in micro-amperes is a micro-ammeter.

amplitude The extent of a vibrator movement measured from the mean position to an extreme.

amplification As a related to detection instruments, the process (either gas, electronic, or both) by which ionization effects are magnified to a degree suitable for their measurement.

angle of incidence The angle formed by the line of an incident ray and a perpendicular line arising from the point of incidence.

angle of lag



53

The angle with which one alternating electrical quantity lags behind another quantity in time, expressed in degrees (1 cycle equals 360) or in radians (1 cycle equals 2 radians).

angle of reflection The angle formed by the line of a reflected ray and a perpendicular line arising from the point of incidence.

angle of refraction The angle formed between the line of a refracted ray and a perpendicular line drawn through the point of refraction.

angular acceleration The time rate of change of angular velocity either in angular speed or in the direction of the axis of rotation. CGS unit: radians/sec .

angular velocity (1) The speed of a rotating object measured in radians per second and generally designated by the lower case Greek letter omega. In the case of a periodic quantity, such as alternating current, the angular velocity is equal to a 2 f. (2) The time rate of angular displacement about an axis. CGS unit: radians/sec. If the

angle described in time is m the angular velocity is =

t, where is in radians, t is in seconds,

and w is in radians per second.

angstrom unit 10 cm, a convenient unit for measuring wavelength of light. Abbreviation: A.

antilogarithm Number from which the log was derived. Obtained as a result of using the inverse procedure of obtaining a log. It is often written as "antilog."

aperture An opening or gap. In optics, the effective aperture is the portion of an objective lens that is actually used.

aplanatic lens A lens that is corrected for spherical, coma, and chromatic aberrations.

apparent power The power value obtained in an alternating current circuit by multiplying the effective values of voltage and current. The result is expressed in volt-amperes, and must be multiplied by the power factor to secure the average or true power in watts.

apsis The point at which an orbiting body is the greatest or least distance from the center of attraction. The greatest distance is called the higher apses and the least distance is called the lower apses.

arc



54

A portion of the circumference of a circle.

Archimedes' principle When a body is placed in a fluid, it is buoyed up by a force equal to the weight of the displaced fluid.

astigmatism (1) A visual aberration caused by lack of sphericity of the cornea. (2) A blurring of the trace of an oscilloscope.

atom Smallest particle of an element that can enter into combination with other elements.

atomic number (1) The number of protons in the nucleus, hence the number of positive charges on the nucleus. (2) The number of protons in the nucleus, hence the number of positive charges on the nucleus. It is also the number of electrons outside the nucleus of a neutral atom. Symbol: Z.

atomic weight The relative weight of the atom of an element based on an atomic weight of 16 for the oxygen atom as the usual chemical standard. The sum of protons plus neutrons is the approximate atomic weight of an atom.

attached method(optics) A method of measuring when all test equipment and standards are physically located on the same reference plane.

Autocollimation A process in which collimated rays of light emanating from an instrument, and carrying the image of a reticule, are aimed at a reflective surface. The reticule image is reflected back into the focal place of the telescope for comparison with the actual reticule as a measure of relative tilt, between the optical axis and the reflective surface. An instrument used for this purpose is called an Autocollimator.

Autocollimator A telescope provided with both an eyepiece and a focal plane target. The basic operating principle is to align a plane with a reflective capability at right angles to the autocollimator axis and/or measure the out-of-squareness of a plane to the autocollimator axis.

autoreflection A process in which the reflected image of a target surrounding the front end of a telescope is compared with the telescope reticle as a measure of relative tilt. (The focal length is twice the dimension from the instrument to reflective surface.)

autumn equinox First day of autumn in the northern hemisphere. It usually falls on September 21st in the northern hemisphere. There are about 12 hours of light and 12 hours of darkness every place on the Earth during an equinox.

average value (1) The value obtained by dividing the sum of a number of quantities by the number of quantities represented.



55

(2) The average of many instantaneous amplitude values taken at equal intervals of time during an alternation (half-cycle). The average value of an alternation of a pure sine wave is 0.637 times its maximum or peak amplitude value.

Avogadro Constant The number of molecules in a kilogram-molecular weight of any substance equals 6.022 X 10

12 kmol.

Avogadro's Law The hypothesis that equal volumes of all gases at the same pressure and temperature contain equal numbers of molecules. Hence the number of molecules contained in 1 cm

3 of any

gas under standard conditions is a universal constant.

Avogadro's Number The number of molecules in a gram-molecular weight of any substance (6.03 x 10

23

molecules); also, the number of atoms in a gram-atomic weight of any element.

axis A straight line, real or imaginary, passing through a body, on which the body revolves.

axis, optical A line formed by the coinciding principal axis of a series of optical elements.

* Note * optical axis as described on pg. 4-6 of OM 3&2 is stated wrong, the glossary is correct.

axis, principal A line through the centers of curvature of a refracting lens.

azimuth Horizontal direction or bearing of one object with respect to another, expressed as an angle measured in a horizontal plane and in a clockwise direction from the north (true north, unless otherwise indicated).

B+ (B plus) The positive terminal of a B battery or other plate-voltage source for a vacuum tube, or the plate-circuit terminal to which the positive source terminal should be connected.

B- (B minus) Symbol used to designate the point in a circuit to which the negative terminal of the plate supply is to be connected.

B-H curve A characteristic curve showing the relation between magnetic induction (B) and magnetizing force (H) for a magnetic material. It shows the manner in which the permeability of a material varies with flux density. Also called "magnetization curve."

backlash A form of mechanical hysteresis (lag) in which there is a lag between the application of a driving force and the response of the driven object.

barn



56

The unit expressing the probability of a specific nuclear reaction taking place in terms of cross-sectional area. It is 10

-24 cm

2 . (See Cross Section.)

barometer An instrument for measuring atmospheric pressure. There is a direct relationship between atmospheric pressure and altitude and many barometers are equipped with an altitude scale. Two types of barometers are "mercury" and "aneroid." The aneroid barometer with an altitude scale is an altimeter.

beam A beam of light can be regarded as the path traced by a small section of an advancing wave front, which is comprised of an infinite number of light rays.

Bernoulli's principle With a fluid in motion, if the velocity is low, the pressure is high and vice versa.

beta The current amplification factor of a transistor when connected in a common-emitter configuration.

beta particle (1) Particle identical to an electron emitted from the nucleus of a radioactive atom. (2) A charged particle emitted from the nucleus and having a mass and charge equal in magnitude to those of the electron.

beta ray A stream of beta particles, more penetrating but less ionizing than alpha rays; a stream of high-speed electrons.

bifilar winding A method of winding a coil in the shape of a coiled hairpin so that the magnetic field is self-canceling and inductance minimized.

bilateral Having, or arranged upon, two sides.

binding energy The energy represented by the difference in mass between the sum of the component parts and the actual mass of the nucleus.

bimetallic element Two strips of dissimilar metal bonded together so that a change in temperature will be reflected in the bending of the element, as a result of differential expansion. Used in thermostats, dial thermometers, and temperature compensating devices in the better pressure gages.

boiling Rapid vaporization which disturbs a liquid, and which occurs when the vapor pressure within a liquid is equal to the pressure on its surface.

bonded strain gage



57

A thin metallic resistance element, usually of wire or foil, chemically cemented to a device being subject to loading or stress. As the load (stress) changes, the electrical resistance of the strain gage changes. Thus, for a fixed value of applied voltage, the output voltage from the strain gage varies in proportion to the strain and provides an indication proportional to the load causing the stress and resultant strain.

bourbon element A curved, hollow tube sealed at one end. When fluid under pressure is forced in the tube it has a tendency to straighten out. With a pointer attached to the sealed end and allowed to move across a scale it becomes a bourdon gage.

Boyle's Law If the temperature of a gas is kept constant, then the volume of the gas will be inversely proportional to the pressure.

bridge circuit An electrical network that is basically composed of four branches connected in the form of a square. One pair of diagonally opposite junctions is connected to the input, and the other pair is connected to the output circuit which contains an indicating device.

bridge rectifier A full-wave rectifier with four elements connected as in a bridge circuit. Alternating voltage is applied to one pair of junctions.

British Thermal Unit (BTU) The amount of heat required to raise the temperature of 1 pound of water 1 Fahrenheit in an ambient environment slightly greater than 39F.

bucking-in To place an instrument so that its line of sight passes through two given points or fulfills two requirements simultaneously. Usually the first operation in setting up control is to establish a width plane.

buoyancy The power to float or rise in a fluid.

buoyant force The upward force which any fluid exerts on a body placed in it.

calibrate To determine by measurement or comparison the correct value of each scale reading on a meter or other device being calibrated. To determine the settings of a control that corresponds to particular values of voltage, current, frequency, or some other characteristic.

calorie The amount of heat required to raise the temperature of 1 gram of water 1 Celsius at 15 Celsius.

candela Unit of luminous intensity. It is of such a value that the luminous intensity of a full radiator at the freezing temperature of platinum (1773C) is 60 candela per centimeter squared. Candela was formerly termed candlepower, or simply candle.



58

capillarity The characteristic of a liquid to be raised or depressed in a tube or small bore. This action is caused by a combination of cohesive, adhesive, and surface tension forces.

celestial Of the sky or the heavens. A celestial telescope is one in which the image appears inverted, as in astronomical telescopes with no erector.

Celsius temperature scale A temperature scale based on mercury in glass thermometer with the freezing point of water defined at 0C and the boiling point of water defined at 100C, both under conditions of normal atmospheric pressure. Formerly called the Centigrade scale.

center of instrument In optics, the intersect point of the vertical, horizontal, and optical axis of a transit or similar instrument when perfectly calibrated.

certify To attest a being true or as represented, or to meet a certain standard.

centripetal force The force required to keep moving mass traveling in a circular path. The force is directed toward the axis of the circular path.

cgs system The common metric system of units (centimeter-gram-second).

chain reaction Any chemical or nuclear process in which some of the products of the process are instrumental in the continuation of magnification of the process.

Charles Law (also Gay-Lussacs Law) The density of an ideal gas at a constant pressure varies inversely with the absolute temperature of the gas.

chemical compound A pure substance composed of two or more elements combined in a fixed and definite proportion by weight.

chromatic aberration A property of lenses that causes the various colors in a beam of light to be focused at various points, this causing a spectrum to appear.

clinometer The clinometer is, in principle, a level mounted on a rotatable member, whose angle of inclination relative to its base can be measured by a circular drum scale.

coefficient of linear expansion The change in unit length in a solid when its temperature is changed 1.



5

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